The Self
The archetypal Self represents "The Whole".
It is tempting to look at everything that pertains to an individual and call it's totality the "Self" but the archetype necessarily refers also to a hidden completeness that is beyond perception. In other words, if it can be perceived or described then it is not really the archetypal "Self".
This archetype is related closely to the concept of "god" for most people. Both "Self" and "god" are concepts that ideally do not have the dualism that is necessarily part of language. So using words to describe them is like using a drawing to describe a new flavor.
As a general rule, the highest ideal a person is aware of points in the direction of the Self, but does not describe it. When a person tries to crystallize, or describe, an ideal, they are preventing it from developing. Like a religious person who talks endlessly about "god" without realizing that the more they try to capture their god with descriptions, the further they are from it, or the lower it (their god) becomes.
Although a person cannot climb on top of the Self, cannot describe nor understand it, they can achieve a balance that lets some aspect of the Self be more visible.
The opposite of Self?
In language (and the thinking that corresponds to it) everything has an opposite. A word cannot be spoken, nor a thought held in the mind, unless it has an opposite. So what is the opposite of Self?
Ideally, the concept "Self" or "god" is unspoken. It is something distant a person can never get close to, an impossible paradox. But assigning a word to it, and describing it, brings some aspect of it into the world of dualism where it must have an opposite.
Basically, the opposite of "Self" is just the opposite of that aspect of it that you have managed to "capture" with words. If, for you, "Self" means "smart" then the opposite would be stupid. If, for you, it means "wholeness" then the opposite of it would be fragmentation. If it means "good" then the opposite would be evil. Etc.
Two historical warnings
Mankind has been studying "Self" and related concepts for thousands of years. In that time, a body of knowledge has developed to prevent dangers. The body of knowledge can be summed up basically in the word "Ethics".
The ethics of religions and other systems are not to make businesses run more smoothly. Their purpose is not to create a tranquil society or make everyone smile. The purpose of ethics is to protect the individual. Each individual.
Two ethical rules that pertain to the study of "Self", and which are found in some form in major religions, are:
1) Don't try to capture a non dualistic "thing". That means understand that there is a boundary between "you" and "nature" and that crossing that boundary is not rewarded by nature. In western religious terms this "ethic" corresponds to "Don't practice sorcery" and "Don't frivolously use words (names) for "god". A parallel warning is "Do not avoid knowledge". For every person who is obedient to an ethic there is a person who avoids learning. Both are equally wrong.
2)